# momentALaD: Moments estimation for the quantile-based asymmetric Laplace... In QBAsyDist: Asymmetric Distributions and Quantile Estimation

## Description

Mean, variance, skewness, kurtosis and moments about the location parameter (i.e., αth quantile) of the quantile-based asymmetric Laplace distribution studied in Gijbels et al. (2019a) useful for quantile regression with location parameter equal to μ, scale parameter φ and index parameter α.

## Usage

 ```1 2 3 4 5 6 7 8 9``` ```meanALaD(mu, phi, alpha) varALaD(mu, phi, alpha) skewALaD(alpha) kurtALaD(alpha) momentALaD(phi, alpha, r) ```

## Arguments

 `mu` This is the location parameter μ. `phi` This is the scale parameter φ. `alpha` This is the index parameter α. `r` This is a value which is used to calculate rth moment about μ.

## Value

`meanALaD` provides the mean, `varALaD` provides the variance, `skewALaD` provides the skewness, `kurtALaD` provides the kurtosis, and `momentALaD` provides the rth moment about the location parameter μ of the quantile-based asymmetric Laplace distribution.

## References

Gijbels, I., Karim, R. and Verhasselt, A. (2019a). On quantile-based asymmetric family of distributions: properties and inference. International Statistical Review, https://doi.org/10.1111/insr.12324.

## Examples

 ```1 2 3 4 5 6``` ```# Example meanALaD(mu=0,phi=1,alpha=0.5) varALaD(mu=0,phi=1,alpha=0.5) skewALaD(alpha=0.5) kurtALaD(alpha=0.5) momentALaD(phi=1,alpha=0.5,r=1) ```

QBAsyDist documentation built on Sept. 4, 2019, 1:05 a.m.